Realistic sectional door animation
Model a single segment e.g.: 



Add an Array and Curve modifier



Now you should be able to animate open/close by translating the x-axis.





Method 2

To avoid that the Curve modifier distorts the segments, you could add another object say plane (Empties cannot have the array modifier) and parent the segment to the plane. Use face duplication on the plane to create the undistorted segements.

Note it is important to apply scale.